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The Zirconium (Z = 40) isotopic chain has attracted interest for more than four decades. The abrupt lowering of the energy of the first $2^+$ state and the increase in the transition strength B(E2; $2_1^\rightarrow 0_1^+$ going from $^{98}$Zr to $^{100}$Zr has been the first example of "quantum phase transition" in nuclear shapes, which has few equivalents in the nuclear chart. Although a multitude of experiments have been performed to measure nuclear properties related to nuclear shapes and collectivity in the region, none of the measured lifetimes were obtained using the Recoil Distance Doppler Shift method in the $\gamma\gamma$-coincidence mode where a gate on the direct feeding transition of the state of interest allows a strict control of systematical errors. This work reports the results of lifetime measurements for the first yrast excited states in $^{98-104}$Zr carried out to extract reduced transition probabilities. The new lifetime values in $\gamma\gamma$-coincidence and $\gamma$-single mode are compared with the results of former experiments. Recent predictions of the Interacting Boson Model with Configuration Mixing, the Symmetry Conserving Configuration Mixing model based on the Hartree-Fock-Bogoliubov approach and the Monte Carlo Shell Model are presented and compared with the experimental data.

The analysis of photometrical observations of comet 29P/Schwassmann-Wachmann 1 is presented. The broadband observations were carried out for 15 nights from 2012 to 2019 at the Lisnyky observational station of Taras Shevchenko National University of Kyiv. Apparent magnitudes and dust productivity level $Af\rho$ in filter R were calculated. Middle and height dust activity of the comet is characterized by parameter $Af\rho$ which varied from 1246 to 17563 cm during all periods of observation. Based on the morphological analysis, four jet-like structures were detected in the coma on almost all dates. Using the geometrical model for the jet structure interpretation during all observation sets, we obtained following results: the nucleus rotation periodof 57\pm2 days, the rotational axis orientation, the locations of active regions for four jet-like structures within a narrow belt near the equator., Comment: 9 pages, 4 figures

Pipelines of state-of-the-art spectrographs dedicated to planet detection provide, for each exposure, series of Cross-Correlation Functions (CCFs) built with a Binary Mask (BM), and the absolute radial velocity (RV) derived from Gaussian fit of a weighted average CCF$_{tot}$ of the CCFs. Here we tested the benefits of the application of the shift finding algorithm developed by Pierre Connes directly to the total CCF$_{tot}$, comparing the resulting RV shifts (DRVs) with the results of the Gaussian fits. In a second step, we investigated how the individual DRV profiles along the velocity grid can be used as an easy tool for detection of stellar line shape variations. We tested this new algorithm on 1151 archived spectra of the K2.5 V star HD 40307 obtained with ESO/ESPRESSO during a one-week campaign in 2018. Tests were performed based on the comparison of DRVs with RVs from Gaussian fits. DRV profiles along the velocity grid (DRV(i)) were scrutinized and compared with direct CCF$_{tot}$ ratios. The dispersion of residuals from a linear fit to RVs from 406 spectra recorded within one night, was found to be $\sigma$=1.03 and 0.83 ms$^{-1}$ for the Gaussian fit and the new algorithm respectively, a significant 20\% improvement in accuracy. The two full one-week series obtained during the campaign were also fitted with a 3-planet system Keplerian model. The residual divergence between data and best-fit model is significantly smaller for the new algorithm than for the Gaussian fit. This new algorithm is an easy tool allowing to obtain additional diagnostics on the RV measurements in series of exposures. It increases the accuracy of velocity variation determinations. Also, departures from constancy of the DRVi profiles, as well as varying differences between RVs from this new method and RVs from a Gaussian fit provide diagnostics of line shape variations due to stellar activity., Comment: 21 pages, 17 figures, to appear in Astronomy and Astrophysics

{\alpha}-RuCl$_3$, a narrow-band Mott insulator with large work function, offers intriguing potential as a quantum material or as a charge acceptor for electrical contacts in van der Waals devices. In this work, we perform a systematic study of the optical reflection contrast of {\alpha}-RuCl$_3$ nanoflakes on oxidized silicon wafers and estimate the accuracy of this imaging technique to assess the crystal thickness. Via spectroscopic micro-ellipsometry measurements, we characterize the wavelength-dependent complex refractive index of {\alpha}-RuCl$_3$ nanoflakes of varying thickness in the visible and near-infrared. Building on these results, we simulate the optical contrast of {\alpha}-RuCl$_3$ nanoflakes with thicknesses below 100 nm on SiO$_2$/Si substrates under different illumination conditions. We compare the simulated optical contrast with experimental values extracted from optical microscopy images and obtain good agreement. Finally, we show that optical contrast imaging allows us to retrieve the thickness of the RuCl$_3$ nanoflakes exfoliated on an oxidized silicon substrate with a mean deviation of -0.2 nm for thicknesses below 100 nm with a standard deviation of only 1 nm. Our results demonstrate that optical contrast can be used as a non-invasive, fast, and reliable technique to estimate the {\alpha}-RuCl$_3$ thickness.

The action of an ideal fluid in Euler variables with a variable number of particles is used for the phenomenological description of the processes of particle creation in strong external fields. It has been demonstrated that the conformal invariance of the creation law imposes quite strict restrictions on the possible types of sources. It is shown that combinations with the particle number density in the creation law can be interpreted as dark matter within the framework of this model., Comment: This article belongs to the Special Issue The Friedmann Cosmology: A Century Later